Gresham/Barlow School District

Mathematics Curriculum Map {Grade: 3rd }

2005/2006

Common

Goals

STANDARDS /FOUNDATIONS/

OSAT ELIGIBLE CONTENT AND CLASSROOM ONLY CONTENT

(Words in bold text are for Classroom Instruction and Assessment only. Italicized words are Eligible Content for items on the OSAT.)

*TIME

FRAME

*UNIT

*TOPICS

*ASSESSMENT

**Vocabulary

 

Mathematical Problem Solving

(current language but under revision)

 

Select, apply, and translate among mathematical representations to solve problems.

 

Apply and adapt a variety of appropriate strategies to solve problems.

 

Monitor and reflect on the process of mathematical problem solving.

 

Communicate mathematical thinking coherently and clearly; use the language of mathematics to express mathematical ideas  precisely.

 

Accurately solve problems that arise in mathematics and other contexts.

CONCEPTUAL UNDERSTANDING

Interpret the concepts of a problem-solving task and translate them into mathematics.

 

PROCESSES AND STRATEGIES

Choose strategies that can work and then carry out the strategies chosen.

 

VERIFICATION

Produce identifiable evidence of a second look at the concepts/strategies/calculations                  to defend a solution.

 

COMMUNICATION

Use pictures, symbols, and/or vocabulary to convey the path to the identified solution.

 

ACCURACY

Accurately solve problems using mathematics.

September-June

Problem Solving

Problem Solving Strategy Focus:

Make an organized list and make a chart or a table

 

Classroom Resources:

(I.)[1] 10 Minute Math Activities and throughout the tasks

 

(S.F.)[2] Problem Solving Transparencies

 

Problem Solving Literature Connections

Sample open-ended prompts available online at www.octm.org to be used as work samples and scored with state scoring guide

 

 

All Standards

September-June

Skill Practice and Review

Math Journals:

2-3 times per week. The problems are set up so that they cycle through all mathematics strands continuously through the year.

 

Classroom Resources:

(S.F.) Spiral Review

 

(S.F.) Assessment Sourcebook: Diagnosing Readiness for Grade 3 pg. 43-46

 

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

 

Compute fluently and make reasonable estimates.

 

 

 

 

Read, write, order, model, and compare up to 6 digit whole numbers.

 

Identify the place value and actual value of digits up to 6 digit whole numbers.

 

Compose and decompose whole numbers less than one thousand by place value.

 

Add and subtract pairs of up to four digit numbers.

 

Mentally add or subtract multiples of 10, 100, or 1000 to or from a number.

 

Identify the operation (add, subtract, multiply, or divide) for solving a problem.

 

Develop and use strategies (overestimate, underestimate, range of estimates) to make reasonable estimates.

 

Recognize which place value will be the most helpful in estimating an answer.

 

Make change for amounts up to $10.00.

 

Order and compare dollars and coins by making equivalent amounts up to $10.00.

 

Sept/Oct

(6 weeks)

Place Value and Addition & Subtraction Review

 

Place value of ones, tens hundreds, thousands

 

Place value concepts involved in additon and subtraction (with regrouping)

 

Addition and subtraction basic facts

 

Relationshis among numbers and fact families. (3+2=5, 2+3=5, 5-3=2, 5-2=3)

 

Addition of 3-digit plus 3-digit whole numbers with regrouping

 

Subtraction of 3-digit minus 3-digit whole numbers with regrouping

 

Rounding one-, two-, or three- digit numbers to the nearst 10, 100, or 1000 for addition & subtraction problems

Concept of odd and even numbers

 

Place values to hundredths place in the context of money

 

Recognition and comparisons for mixed amounts of pennies, nickels, dime quarters, half-dollar and dollar coins up to $10.00

 

Money word problems with and without regrouping up to $10.00

 

Location of numbers and addition & subtraction on a numberline

 

+/- Inverse Operations (positive & negative numbers)

 

September Calendar: [3]

?       Counting by 2?s pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day ~ Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

 

Math Stations:[4] 

Students particpate in games and activities that focus on building and recording numbers up through 1,000, addition and subtraction with regrouping, and addition and subtraction of money amounts up through $10.

 

 

Classroom Resources:

(I.) Combining and Comparing Book, Up and Down the Numberline, Landmark in the Hundreds Inv. 2 & 3, Mathematical Thinking at Grade 3 Inv. 2

 

(S.F.) Ch. 1, Ch. 2 Ch. 3 and Ch. 10

Place Value and Addition and Subtraction Literature Connections

(I.) Assmt. Masters: 1, 2, 5, 28-31, 33-36

Ordinal number

 

Digit

 

Decimal point

 

Decimal number

 

Expanded form

 

Commutative property

 

Associative property

 

Equation

 

Expression

 

Inequalities

 

 

 

 

Understand patterns, relations, and functions.

 

Represent and analyze

mathematical situations

and structures using algebraic

symbols.

 

Analyze characteristics and properties of                                         two- and three-dimensional geometric                                         shapes and develop mathematical                                           arguments about geometric relationships.    

 

Use visualization, spatial

reasoning, and geometric

modeling to solve problems.

 

Specify locations and describe

spatial relationships using

coordinate geometry and other

representational systems

 

Apply transformations and use

symmetry to analyze

mathematical situations.

 

 

Describe, extend, and make generalizations about numeric and

geometric patterns (e.g., increasing the number of sides of

 two-dimensional geometric figures in sequence; consecutive

odd numbers).

 

Supply a missing element in or determine a rule that extends number

patterns involving addition and multiplication by a single-digit

number.

 

Generate a pattern or sequence from a verbal, written, and pictorial

description.

 

Use letters, boxes, or other symbols to stand for a missing number in

simple expressions or equations.

 

Identify, describe, compare, and classify common three-dimensional

geometric objects: cubes, prisms, spheres, pyramids, cones, and

cylinders.

 

Compare and classify solid geometric shapes (e.g., triangular,

pyramid, cube, rectangular prism) according to the number and

shapes of faces, edges, and vertices.

 

Recognize and identify attributes of three-dimensional geometric

shapes (faces, edges, vertices), including attributes of shapes in the

environment.

 

Model three-dimensional shapes including cubes, rectangular

prisms, spheres, pyramids, cones, and cylinders.

 

Put shapes together and take them apart to form other shapes.

 

Recognize three-dimensional geometric shapes (e.g., cube, cone,

cylinder, pyramid, and sphere) in the environment and from

different perspectives.

 

Describe paths for moving from one location to another on a grid.

 

Identify line and rotational symmetry

 

Predict and describe the results of performing reflections, rotations

and translations of triangles.

 

 

 

 

 

Oct/Nov

(6 Weeks)

Geometry and Patterning

Perimeter of geometric shapes such as triangles, quadrilaterals (trapezoid, paralellogram, rectangle, rhombus, square), pentagons, hexagons, octagons, in meters and centimeters

 

Missing elements in a geometric pattern

 

Attributes of geometric figures 

 

Properties of geometric figures (Congruence and Similarity)

 

Reflections and  rotations of line segments, angles, triangles, quadrilaterals, circles (including location of diameter & radius),

 

Explore turns and pathways

 

Recognition and description of line segments, angles (acute, right, obtuse), spheres, cubes, prisms, and pyramids

 

Angle Identification (acute, obtuse, 90?)

 

Closed and not-closed figures

 

3-dimensional shapes shown "unfolded" in 2-dimensional representations

 

Line and rotational symmertry

 

October Calendar:

?       Counting by 3?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day: Area and Perimeter Comparisons                                      (words are selected from the grade level vocabulary

          bank),

?       About Time: What time will it be 3 minutes from

?       now? 3 minutes ago?

 

November Calendar:

?       Counting by 4?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       About Time: Daily Schedule (duration of

         time in minutes and hours)

 

Math Stations:

Students participate in games and activities that focus on geometric patterning, perimeters, coordinates, and translations and symmetry

 

Classroom Resources:

(I.) Flips, Turns, and Area, Exploring Solids and Boxes, Turtle Paths

 

(S.F.) Ch. 8, and 4-9 pg. 218

 

Geometry Literature Connections

(I.) Assmt. Masters: 2, 13-16, 38-40, 47-50

Growing pattern

 

Expression

 

Plane

 

Vertex

 

Parallel lines

 

Acute angle

 

Right angle (90?)

 

Flip

 

Congurence

 

Slide

 

Symmetry

 

Ordered pair

 

 

Compute fluently and make reasonable estimates.

 

Understand meanings of operations and how they relate to one another.

 

Apply transformations and use symmetry to analyze mathematical situations.

 

 

 

Develop and evaluate strategies for multiplying whole numbers.

 

Develop and acquire efficient strategies for determining multiplication and division facts 0-9.

 

Find areas of rectangular arrays.

 

Represent situations using models of multiplication and division (e.g., repeat addition, equal groups of objects, arrays, repeated subtraction, equal grouping, sharing equally)

 

Use the commutative and associative properties of multiplication to simplify calculations

 

Describe the effects of multiplying or dividing by a whole number.

 

Demonstrate the zero property for multiplication and identity property for multiplication and division.

 

Multiply a two-digit number by a one-digit number.

 

Demonstrate the counting skills of skip counting as they relate to multiplication facts.

 

Dec/Jan

(7 Weeks)

Multiplication and Division

Skip counting and the concept of multiples

 

Area of arrays

 

Multiplication basic facts

 

Division basic facts

 

Reproduction of a pattern in multiples of the numbers 2 through 9, monetary relationships under $10.00, relationships between numerator and denominator of a fraction using common multiples, divisions or arrangements of two dimensional geometric figure

 

Relationship between two quantities such as number of people who can be seated at a table & the number of tables needed

 

Mathematical relationships and patterns in table format

 

Factors in equations ( __ x 5 = 15)

 

Multiplication patterns on the 100s Chart and with a calculator constant

 

Multiplication and division basic facts strategies

 

December Calendar:

?       Counting by 5?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       About Time: What time was it 6 hours ago? What time will it be in 6 hours?

 

January Calendar:

?       Counting by 6?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       Measurement Records: Temperature Highs and Lows Chart and Line Graphs

?       About Time: time comparison between time here and Portland, Maine

 

Math Stations: 

Students particpate in games and activities that focus on multiples on the calculator, multiplication and division basic facts through nine

 

Classroom Resources:

(I.) Things that Come in Groups and Mathematical Thinking at Grade 3 Inv. 2

 

(S.F.) Ch. 5, 6, and 7

 

Multiplication and Division Literature Connections

(I.) Assmt. Masters: 7-11

Multiple

 

Identity

 

Array

 

Factors

 

Square number

 

Remainder

 

Compute fluently and make reasonable estimates.

 

Represent and analyze mathematical situations and structures using algebraic symbols.

 

Multiply a two-digit number by a one-digit number.

 

Identify the operation (add, subtract, multiply, or divide) for solving

a problem.

 

Develop and use strategies (overestimate, underestimate, range of estimates) to make reasonable estimates.

 

Recognize which place value will be the most helpful in estimating an answer.

 

Identify and apply a relationship between two quantities (e.g., If four people can be seated at one table, how many tables are needed to seat 24 people?).

 

Feb

(4 Weeks)

Larger number multiplication, Mixed Practice Review and Estimation

Multiplication facts through twelves

2 digit multiplcation

 

Mixed Practice and 2-Step Story Problems using Student and Teacher Generated Word Problems (All Operations)

 

Estimation Strategies

 

February Calendar:

?       Counting by 7?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       Measurement Records: (foot, yards, counting by 12)

?       About Time: Sunrise and Sunset Times (duration of time in minutes and hours of daylight)

 

 

Math Stations:

Students particpate in games and activities that focus on creating and solving story problems, rounding and estimations skills, and mixed operations practice games

 

Classroom Resources:

(I) Landmarks in the Hundreds and Things that Come in Groups

 

(S.F.) Ch. 11 plus story problem examples can be found throughout Ch 2, 3, 5, 6, 7 that can be modified to fit teacher purposes

 

(I.) Assmt. Masters: 21,23-26

 

 

Select and use appropriate statistical methods to analyze data.

 

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

 

Develop and evaluate inferences and predictions that are based on data.

 

Determine the mode and range of a set of data.

 

Ask and answer simple questions that can be answered by collecting, organizing,              and displaying data.

 

Represent and interpret data using tally charts, pictographs, and bar graphs, including identifying the mode and range.

 

Draw conclusions and make predictions and inferences from tally charts, pictographs, or bar graphs.

 

 

March/April

(4 Weeks)

 

Statistics

Data analysis from charts or tables with five or fewer entries, horizontal & vertical bar graphs with five or few bars, & pictographs with 10 or fewer data pieces (data limited to whole numbers up to 200, whole dollar amounts up to $100)

 

Graph creation using pencil/paper and computer software

 

Mode

 

Range

 

Possible Outcomes

 

March Calendar:

?       Counting by 8?s Pattern,

?       # of Days in School using Base Ten pieces,

?       Class Bank: +25? for each day of school,

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       Measurement Records: (pounds, ounces, grams)

?       About Time: What was the time 19 hours ago? What were you doing then?

?       Measurement tool riddles ( e.g. I measure length. I have 100 units. What am I?  A.  A meter stick.)

 

Math Stations:

Students particpate in games and activities that practice probability concepts and data collection using charts and graphs

 

Classroom Resources:

http://www.pps.k12.or.us/instruction-c/math/01_02_lesson_plans/3probability.pdf

 

(S.F.) Ch. 4 Sections B & C

Ch. 12 Section B

 

Statistics and Probability Literature Connections

 

Survey

 

Line plot

 

Mode

 

Pictograph

 

Range

 

Line graph

 

Coordinate graph

 

Probability (chance)

 

 

 

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

 

Understand measurable attributes of objects and the units, systems, and processes of measurement.

 

Apply appropriate techniques, tools, and formulas to determine measurements.

 

 

 

 

Order, model, compare, and identify commonly used fractions (halves, thirds, fourths, eighths, tenths) using concrete models and visual representations.

 

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

 

Locate whole numbers and common fractions on a number line.

 

Select the most appropriate tool and metric unit to measure length, time, weight, and volume.

 

Compare units of measure between customary and metric systems (e.g., inches > centimeters, liters < gallons).

 

Understand and explain the need for using standard units.

 

Determine elapsed time for given activities using representations of analog and digital clocks.

 

Tell time to the nearest minute using an analog clock.

 

Describe temperature changes and concepts as they occur in daily situations.

 

Determine measurements of length to the nearest centimeter and nearest meter.

 

Estimate the length of objects in meters and centimeters.

 

Determine measurements of volume to the nearest milliliter or liter of measuring cups, beakers, or graduated cylinders.

 

Estimate volume of objects in milliliters and liters.

 

Determine measurements of weight to the nearest gram and kilograms.

 

Estimate weight of objects in grams and kilograms.

 

Find areas of rectangular arrays.

 

Apr/Jne

(8 Weeks)

Fractions & Measurement

Linear measures using metric units

Weight measures using metric units

Volume/capacity measures using metric units

Comparison between customary and metric units using real world referents

Time

Temperature

 

April Calendar:

?       Counting by 9?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25? for each day of school

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       Fraction a Day Pattern Block Numberline (fraction notation, equivalence, mixed and improper fraction notation)

?       Geometry Riddles: What am I?  (e.g. I have a right angle, I have 3 sides. What am I? A. An equilateral triangle?)

 

May/June Calendar:

?       Counting by 10?s Pattern

?       # of Days in School using Base Ten pieces

?       Class Bank: +25 cents for each day of school,

?       Word for the Day: Area and Perimeter Comparisons (words are selected from the grade level vocabulary bank)

?       Fraction a Day: Pattern Block Numberline (fraction notation, equivalence, mixed and improper fraction notation)

?       Money Riddles: (e.g. I have __ coins. I have ___ cents. What coins do I have? )

 

Math Stations:

Students particpate in games and activities that reinforce fraction concepts and measurement skills

 

Classroom Resources:

(I.) From Paces to Feet, Fair Shares

Portland Public Supplemental Packet at: http://www.pps.k12.or.us/instruction-c/math/01_02_lesson_plans/3measurement.pdf

 

(S.F.) Ch. 9, Ch. 10 Ch. 12 Section A

 

Fraction and Measurement Literature Connections

(I.) Assmt. Masters: 18-20, 42-96